Devil facial tumour 1 (DFT1) is a transmissible cancer clone endangering the Tasmanian devil. The expansion of DFT1 across Tasmania has been documented, but little is known of its evolutionary history. We analysed genomes of 648 DFT1 tumours collected throughout the disease range between 2003 and 2018. DFT1 diverged early into five clades, three spreading widely and two failing to persist. One clade has replaced others at several sites, and rates of DFT1 coinfection are high. DFT1 gradually accumulates copy number variants (CNVs), and its telomere lengths are short but constant. Recurrent CNVs reveal genes under positive selection, sites of genome instability, and repeated loss of a small derived chromosome. Cultured DFT1 cell lines have increased CNV frequency and undergo highly reproducible convergent evolution. Overall, DFT1 is a remarkably stable lineage whose genome illustrates how cancer cells adapt to diverse environments and persist in a parasitic niche.